The Most Valuable Everyday Math Skill

  • by Brett Berry - Wed, 06/01/2016 - 06:13

Percentages. They come up all the time, in the most casual places. While shopping, dining out, grabbing a latte, checking grades, banking, taxes, … need I go on?

That makes them the most valuable everyday math skill I can teach you.

I’m proud to say my mom taught me this trick when I was very young. We’d spend Saturdays shopping clearance racks and she’d quiz me over and over again, having me calculate the discounts in my head. Needless to say, I got pretty darn good with percents!

I cannot stress enough how much I want you to master this!

The next time you’re out dining, I want you to fill in the tip on your receipt with confidence and gusto and without even one glance at your phone calculator.

A Little Trick

A percent represents how many of something there are per 100, e.g. 15% means fifteen per one-hundred.

Of course most of the time we are not taking a percentage of 100, but of a different value.

For example, let’s begin by finding 10% of 250.

The 10% Trick

To calculate 10% of a number, move the decimal point one position left.

Here are some examples to illustrate:

Note the decimal point is always immediately after the one’s place, even if not shown.

Why does this work? Let’s take a closer look.

Suppose we were calculating 10% of 250 long-hand. I would begin by rewriting 10% as 10/100 and swap out the keyword of for a multiplication symbol.

Then reduce 10/100 by canceling the factors of 10.

When learned that when dividing by 10, we move the decimal point one place to the left. Therefore,

Calculating Restaurant Tips

Using our trick, we can calculate common tip percentages of 10%, 15% and 20% mentally.

Suppose your dinner bill comes to $48.50.

10% Tip Mentally

To find 10%, use the 10% trick and move the decimal point one place left.

15% Tip Mentally

To calculate 15%, we combine 10% and 5% of $48.50.

5 percent is half of 10 percent. So 5 percent of $48.50 will be half of 10 percent of $48.50.

Note I rounded $2.425 to the nearest penny, $2.43

For practical purposes you can approximate the tip, so feel free to round this up to $2.50.

Finally combine the 10 percent with the 5 percent value. Using rounded values to approximate 15% we obtain:

Which is only 22 cents away from the exact value of 15% of $48.50.

20% Tip Mentally

Suppose we’d like to tip 20%. To do this we’ll double our 10 percent value because 2 x 10 percent = 20 percent.

Again we may wish to approximate instead.

Therefore, approximately 20% of $48.50 is $10.

Calculating Discounts

Another everyday scenario where you might encounter percents is while shopping.

For example, suppose we have a sub-total of $168.75. Let’s calculate a variety of possible discounts.

10% off

First take 10 percent of $168.75.

Note we rounded $16.875 to the nearest penny, which is $16.88

Since it is 10% off, subtract $16.88 from $168.75.

An estimate will suit our purposes so round $168.75 and $16.88 to the nearest dollar and then subtract.

Our estimation is very close, only 13 cents over the exact answer.

25% off

Now let’s try 25% off.

We have two options for finding 25% mentally:

  1. 25% is one-fourth of 100 percent, so we may divide our total by 4.
  2. we may compose 25% by adding two 10%’s and one 5%.

Option One:

For our purposes, an estimate is fine so let’s begin by rounding $168.75 to $170. I’ll then use strategic division to divide $170 mentally.

Note: If you struggle to perform those divisions mentally, you may wish to split them into pieces and divide individually. For example, 170 = 160 + 10.

Which yields

Likewise, $85 ÷ 2 can be split apart and divided individually by 2 to yield $42.50.

So $42.50 is 25% of $170. Hence our total after discount is approximately $127.50.

Option Two:

Using this method we’ll compose 25% from 10% and 5%.

First, approximate 10% of $170.

Secondly, find 5% by dividing 10% in half.

Now we’ll combine two 17’s and an 8.5 to obtain an approximation for 25%.

Again, we arrived at a discount of $42.50, which yields a total of $127.50.

30% off

To calculate 30%, we need to add together three 10%’s. We’ve already approximated 10% as 17, so simply add three 17’s together.

Notice I added 17 in stages to make it easier to sum mentally

Therefore 30% off is $51 off. Meaning that the total after discount is approximately $119.

Mentally, I subtract $51 by first subtracting the tens and then the ones

50% off

Fifty percent is simply half off. So all we need to do is divide 170 by 2.

Therefore, the total after discount is $85.

That’s a great start! These techniques will aid you in most percentages you’ll experience day-to-day. In the next lesson, we’ll take an in depth look at how to mentally calculate percentages to the exact percent.

 

Brett Berry is a math evangelist who writes a math blog for Medium.com called Math Memoirs.